Best Known (70, 70+48, s)-Nets in Base 5
(70, 70+48, 252)-Net over F5 — Constructive and digital
Digital (70, 118, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (70, 120, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 60, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 60, 126)-net over F25, using
(70, 70+48, 6679)-Net in Base 5 — Upper bound on s
There is no (70, 118, 6680)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 30103 284334 038253 363556 525173 628319 693134 970756 742684 782702 001947 975158 251084 278785 > 5118 [i]